[R] boxplot $conf

[Liaw, Andy]

> From: CJSwanepoel at t-online.de [mailto:CJSwanepoel at t-online.de]
> 
> Hello R-Help,
> 
> Could anybody tell me how the boxplot-function calculates the upper
> and
> lower extremes of the notch contained in $conf which I assume is the
> confidence interval? Is it reliable for data which is not normally
> distributed? If not, how can I calculate and boxplot a specific
> confidence interval for not normally distributed data in R (increasing
> the sample size does not normalize the sample distribution)?

Looking at the body of the function boxplot.stats, the CI for median (the
notches in the boxplot) is calculated as:

  median +/- 1.58 * box length / sqrt(n)

where box length is roughly the IQR (75th percentile - 25th percentile)
[technically, it's the "H-spread").  Description and explanation can be
found on page 79 of "ABC of EDA" by Vellman & Hoaglin.  It's based on normal
approximation, but for large sample this is suppose to be a very good
approximation.

HTH,
Andy

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